I am a newbie in Optimization. I have this Optimization problem, could anyone help how can I analyze it and solve it?
\begin{align}\label{Problem_formulation} \mathbb P_1& ~~~~~~\mathop{\max}_{{ \eta, x_0 }} ~~~~{B}\log _2 \left(1+ \frac{{{P_M}\Vert {\textbf g}_d\Vert ^2}{( {\frac{c}{{4\pi {q}}}} )^2 {x_3}^{ - 2}{e^{ - K{x_3}}}}} {{{\sigma_w^2}}}\right)+\sum\nolimits_{f = 1}^{[S/\eta ]} \frac{{{f^{ - \delta }}}}{{\sum\nolimits_{f = 1}^{[S/\eta ]} {{f^{ - \delta }}} }}~~{B}\log _2 \left(1+ \frac{{{P_S}\Vert {\textbf h}_1\Vert ^2}{( {\frac{c}{{4\pi {q}}}} )^2 {x_0}^{ - 2}{e^{ - K{x_0}}}}} {{{\sigma_w^2}}}\right)\nonumber \\ &\mathop{\rm{s.t.}} \;\;~\eta \in [0,1], ~~ \forall f \in F \nonumber\\ &\;\;\qquad \sum\nolimits_{f = 1}^{[S/\eta ]} {b_f} \leq S \end{align}
System parameters
- System bandwidth $B = 10^{6}$
- Number of files $F = 10^{4}$
- SBS cash capacity $S = 100$
- MBS-user distance $x_{3} = 15$
- Noise power in Watts $\sigma = 10^{-90/10}$
- Light speed $c = 3 \cdot 10^{8}$
- Operating frequency $q = 10^{12}$
- Molecular absorption coefficient $K = 0.0016$
- Path loss exponent for NLOS direct link MBS-user $\alpha_{N} = 4$
- Path loss exponent for LOS link SBS-user $\alpha_{L} = 2$
- Transmit power MBS in Watts $P_{M} = 10^{30/10}$
- Transmit power SBS in Watts $P_{S} = 10^{30/10}$
- Direct link MBS-user gain $G_{gd} = 4$
- LOS link SBS-user gain $G_{h} = 4$
- Skewness factor $\delta = 1$
I plot the function to see its curve: